Question

Show that any posite odd integer is of the form 6q+1 or 6q +3 or 6q +5 where q is some ineger

Answer 1

Answer:

Let a be any positive integer b = 6

so,

a = bq + r

( 0 less or equal to r less than or equal to 6)

r = 0,1,2,3,4,5

odd r = 1,3,5

Case 1

r = 1

a = 6q + 1 ___(1)

Case 2

r = 3

a = 6q + 3 ___(2)

Case 3

r = 5

a = 6q + 5 __(3)

so,

from the above equations (1), (2), (3) it is proved that any odd positive integer is of the form 6q+1, 6q+3, 6q+5.